Problem: Solve for $x$ : $ 2|x + 5| - 2 = 3|x + 5| + 5 $
Subtract $ {2|x + 5|} $ from both sides: $ \begin{eqnarray} 2|x + 5| - 2 &=& 3|x + 5| + 5 \\ \\ {- 2|x + 5|} && {- 2|x + 5|} \\ \\ -2 &=& 1|x + 5| + 5 \end{eqnarray} $ Subtract $5$ from both sides: $ \begin{eqnarray} -2 &=& 1|x + 5| + 5 \\ \\ {- 5} && {- 5} \\ \\ -7 &=& 1|x + 5| \end{eqnarray} $ Simplify: $ -7 = |x + 5| $ The absolute value cannot be negative. Therefore, there is no solution.